In the literature, bank runs take the form of withdrawals of real demand deposits that deplete a fixed reserve of goods in the banking system. This framework describes the type of bank run that has occurred historically in the United States and more recently in developing countries. However, in a modern banking system, large withdrawals take the form of electronic payments of inside money, with no analog of a depletion of a scarce reserve from the banking system. In a new framework of nominal demand deposits repayable in inside money, pure liquidity-driven bank runs do not occur. If there were excessive early withdrawals, nominal deposits would hedge the bank, and flexible monetary prices in the goods market would limit real consumption. The maturity mismatch of short-term liabilities and long-term assets is not sufficient for multiple equilibria bank runs without other frictions, such as problems in the interbank market. A key role of the bank is to ensure optimal real liquidity, allowing markets to optimally distribute consumption goods through the price mechanism.